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07 Aug 2018 18:19

vlad01 wrote:
I don't know how much it would effect the outcome but M class stars are entirely convective so they will eventually fuse practically all their Hydrogen and continue as a Helium burning convective star. But one thing is the rate they fuse at is so much slower than the core fusion stars, in order of 100s of billions of years, perhaps into the trillions. They also happen to be quite common.

In the long run, M-class stars would not really affect the ratio of elements in the universe. The big ones may create a surplus of elements as they die, but the smaller ones have a quieter death in the form of a helium white dwarf (which do not exist yet due to the vast timescales required for their inception, as you said), and do not release as many 'useful' elements. More massive stars could continue to fuse helium into carbon, carbon into oxygen, oxygen into silicon and silicon into iron. So-called 'Iron Stars'  could be the end result, though these are more theoretical since of course we have no examples of these in the observable universe. In the very, very, very end of the universe, only black-holes would exist, sucking up anything that is nearby, before ripping themselves apart by their own Hawking radiation. Then the universe may enter a high entropy state of quantum vacuums. Maybe.
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07 Aug 2018 23:22

midtskogen wrote:
Source of the post I calculated that I've spent just over a week airborne over the past 12 months covering a distance of about half a light second.  Does this also mean that I've travelled half a second further into the future than if I'd remained at home, or is the maths more complicated?

Yes, it is more complicated.  The time dilation effect depends on both the distance traveled in space and the time it took.  I confirm FFT's calculation that you experienced about 200 nanoseconds less time due to special relativity.

However, vlad is also right that your clock ticks faster because of your flight altitude, and at your speed and altitude, this works out to be even stronger than the special relativistic effect.  Assuming the airplane's average cruising altitude is about 10,000 meters, and you flew 0.5 light seconds at 250m/s (about 7 days continuous flying), then you experienced about 650 nanoseconds more time due to general relativity.

So the combined effect is that you aged about 450 nanoseconds more than the rest of us. :P
 
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08 Aug 2018 00:22

Thanks.  I suspected it was more complicated, but not that the altitude would more than cancel it, since 10km is not much at the scale of the earth.  There's another thing to consider: latitude.  It's perhaps the most important variable?
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08 Aug 2018 01:41

midtskogen wrote:
Source of the post There's another thing to consider: latitude.  It's perhaps the most important variable?

Very surprisingly, no!  A point on the equator rotates about the center faster, which would make us think clocks tick slower there. But the equator also bulges outward due to Earth's spin, bringing it farther from the center, which makes clocks tick faster.  These cancel exactly.  Time dilation on Earth is completely independent of latitude. :)

There is a wonderful article, written as a sort of Socratic dialogue, which explains beautifully why these would cancel exactly.  In short it uses the equivalence principle, and the fact that the Earth's surface is an equipotential surface.  That is, the Earth's surface takes on a shape which is "level" (besides the terrain of mountains and valleys) when we consider gravitation plus centrifugal forces together. And by the equivalence principle, no local experiment can distinguish between centrifugal force or actual gravity, so we must treat their effects the same, and the time dilation would be the same across the surface.  Only the mountains and valleys contribute a variation.

The Equivalence Principle as a Stepping Stone from Special to General Relativity: A Socratic Dialog

Preview:
I. SETTING THE SCENE
Sam is in the office and has just finished reading Plato’s Meno1 in which Socrates uses a self-discovery technique to teach a boy Pythagoras’ theorem. Sam is inspired by this dialog and is pondering its applicability to lecturing undergraduate physics when a tap on the door breaks that chain of thought. Kim enters the room looking bleary eyed and pale. “Been out celebrating the last lecture of the year” Sam surmises, little knowing that other things have kept Kim awake.

II. THE DIALOG
Kim:
Your lectures on special relativity fascinated me, and when I got home I wondered if I could construct a simple experiment to prove or disprove time dilation, the aspect of special relativity that interests me the most. While lying in bed before dozing off I realised that a clock placed at the equator should run slower than a clock placed at the pole. So I did a little calculation and found that special relativity predicts that a clock on the equator runs slower by about 100 nanoseconds per day with respect to a clock at the pole. While this effect is not large it is certainly measurable with modern atomic clocks. So I went onto the internet to see if I could find any reference to such an experiment and to my surprise I couldn’t.

I was starting to get so frustrated that I couldn’t sleep. I glanced at the clock (3am). I thought to myself “How accurate is my clock? I should check it against internet time.” Then it occurred to me that the world timing standard organisations must mention a latitude effect on local clock accuracies. So I got onto the internet again and checked The Bureau International des Poids et Mesures (BIPM)2 as they calculate the international atomic time (TAI). BIPM calculate TAI from atomic clocks located in more than 30 countries around the world. I was sure that I must find something about the latitude effect on their web site. After spending hours trawling through the site and then other sites on the web, I came up with nothing. There was a discussion of the relativistic effect of placing clocks at high altitudes, but nothing about latitude. In my despair I gave up and collapsed into a fitful sleep. I came to see you today in the hope that you could cure my insomnia.
 
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midtskogen
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08 Aug 2018 04:15

Interesting.  So, one could say that the Earth's bulge around the equator is a relativistic effect?
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08 Aug 2018 04:45

That's an interesting way to put it.  I don't normally think of it that way, but I suppose the logic could be expressed in either direction, like saying that gravity is things trying to go to where time passes the most slowly. :)
 
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08 Aug 2018 08:27

vsause did a great video on that very concept.
 
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08 Aug 2018 13:08

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09 Aug 2018 00:20

While playing around with time dilation formulas, I just came across something interesting.

If a ship is in a circular orbit at exactly 1.5 times the planet's radius (this is 3185km altitude for Earth), then its clocks will tick at exactly the same rate as clocks on the planet surface.  For a closer orbit, special relativity dominates and the orbiting clock will tick slower due to its speed, and for higher orbits general relativity dominates and it ticks faster due to the weaker gravity.

So for astronauts on the ISS (about 400km altitude), time is slower for them (by about 25 microseconds per day!) while for orbiting GPS satellites (roughly circular orbits at about 20,000km altitude), time is faster than on Earth (by about 38 microseconds per day).  This actually must be accounted for in order for GPS to work properly, since the system requires extremely precise time measurements to pinpoint your location to within a few meters.  Light travels about 0.3 meters per nanosecond, so if GPS did not account for time dilation then it would accumulate an error of 11 kilometers per day!

These corrections were actually built into the global positioning system from the outset, so the fact that GPS did not fail immediately is a nice proof that time dilation is real. :)
 
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09 Aug 2018 01:57

Yes GPS satellites use atomic clocks and do offset the time to account for this to ensure accuracy for devices back here on Earth.
 
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midtskogen
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09 Aug 2018 05:26

Watsisname wrote:
Source of the post If a ship is in a circular orbit at exactly 1.5 times the planet's radius (this is 3185km altitude for Earth), then its clocks will tick at exactly the same rate as clocks on the planet surface.

For a planet and moon system with equal density, isn't that coincidentally also the Roche limit?
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09 Aug 2018 06:42

In some case it is close, but not exactly.  The definition of the Roche limit is rather fuzzy and depends on some assumptions about the structure and rotation of the moon.  

If we assume the moon is very rigid and it is the same density as the planet then the Roch limit is about 1.26 times the planet's radius.  It becomes 1.44 radii if we include tidal locking, and grows to 2.4 radii if we treat the moon as a fluid.

Added:
midtskogen wrote:
Source of the post I suspected it was more complicated, but not that the altitude would more than cancel it, since 10km is not much at the scale of the earth.

I think this is also worth pointing out -- it is indeed not obvious that 10km would make such a difference.  But here's one way to think about it:  Earth's average radius is 6371km, so moving up 10km is a 0.16% change.  But 250m/s is only 0.000083% of the speed of light.  Looked at in this way, perhaps it's less surprising that the general relativistic effect can dominate for air travel.

However, it is more complicated than that.  The mass (or density) of Earth also matters.  A less dense Earth would make the 10km gain in altitude less significant.  If Earth was the same size but 1/3 of the mass, then the special and general relativistic effects would have more neatly cancelled on your air travel.  (Of course a 1/3 as massive Earth might change how air travel works, among other problems). :P
 
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09 Aug 2018 07:47

midtskogen wrote:
Source of the post For a planet and moon system with equal density, isn't that coincidentally also the Roche limit?

If I use the Earth's radius that Google gives me (6371 Km), the Roche limit for objects with equally density is 8026.957 km. (According to my calculation.) That would be about 1.26 times the radius.


(Watsisname was faster ...)
 
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09 Aug 2018 10:32

An'shur wrote:
I came across an interesting video. I am wondering how could I calculate the orbital period of the configuration at 3:32. I know all of these are three body orbits which are unstable, but the one I am interested in appears to be doable in Space Engine.


Edit:
► Show Spoiler

I might have been overlooked :)

FastFourierTransform wrote:
Source of the post ...star formation would cease even if astronomical amounts of Hydrogen would still be present in the darkness of the Universe.

That is counterintuitive (like many things in the universe), but I think your assumption makes sense. Thanks for the analysis of the problem.
 
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09 Aug 2018 10:59

Watsisname wrote:
While playing around with time dilation formulas, I just came across something interesting.

If a ship is in a circular orbit at exactly 1.5 times the planet's radius (this is 3185km altitude for Earth), then its clocks will tick at exactly the same rate as clocks on the planet surface.  For a closer orbit, special relativity dominates and the orbiting clock will tick slower due to its speed, and for higher orbits general relativity dominates and it ticks faster due to the weaker gravity.

So for astronauts on the ISS (about 400km altitude), time is slower for them (by about 25 microseconds per day!) while for orbiting GPS satellites (roughly circular orbits at about 20,000km altitude), time is faster than on Earth (by about 38 microseconds per day).  This actually must be accounted for in order for GPS to work properly, since the system requires extremely precise time measurements to pinpoint your location to within a few meters.  Light travels about 0.3 meters per nanosecond, so if GPS did not account for time dilation then it would accumulate an error of 11 kilometers per day!

These corrections were actually built into the global positioning system from the outset, so the fact that GPS did not fail immediately is a nice proof that time dilation is real. :)

This raises an interesting point as to the affects of time dilation, as I remember reading about that famous experiment involving the ISS astronaut Scott Kelly staying aboard the ISS for 520 days — all of which he spent zooming around Earth at 17,500 mph (28,160 km/h). When he came back do to Earth, he was 6 minutes and 5 milliseconds younger then his twin brother, Mark. I'm surprised this 'twins study' was not brought up earlier in this topic.
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